P + E PE P + E P + E P E P + E (a) Assume that all reaction steps obey mass-action kinetics. What is the steady-state dependence of P as a function of the concentration of E ? (Assume that total amount of E E , and P are all constant and that P is in excess compared to E and E ). (b) Alternate starting point for problem: you should be able to rearrange the solution as follows where V is proportional to the total E in the system, E is proportional to the total V in the system, P is the total protein concentration (in all forms), and K and K are suitable combination of the rate constants for the reactions previously described. For K = 1.0, K = 1.0, plot the steady- state locus of solutions for P* /P versus V / V . (c) Assume that the two enzymes operate in a saturated regime, that is m the reactions follow zero-order kinetics with respect to the enzymes. Use the expression from part (b) to plot the steady-state locus for this extreme situation(i.e., K = 0, K = 0). (d) Comment on the difference in shape of the gain functions in parts (b) and (c). Based on the initial problem description, explain how biology can produce switchlike behavior in this system.
P + E PE P + E P + E P E P + E (a) Assume …
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